Question

a 13kg block is at rest on a level floor. A 400 g glob of putty is thrown at the block so that the putty travels horizontally, hits the block, at sticks to it. The block and putty slide 15cm along the floor. if the coefficient of sliding friction is 0.4, what is the initial speed of the putty

Answer 1

36.3m/s

Step-by-step explanation:

We are given that

Mass of block, m=13 kg

Mass of glob,m'=400g=0.4 kg

1 kg=1000g

Total mass, M=13+0.4=13.4 kg

Distance, s=15 cm=0.15m

1m=100cm

Coefficient of sliding friction,
`\mu=0.4`

We have to find the initial speed of the putty.

Friction force, f=
`\mu Mg=0.4* 13.4* 9.8`N

Where
`g=9.8m/s^2`

Work done=
`Fs`

Work done=
`0.4* 13.4* 9.8* 0.15`

Work done=7.8792 J

Work done =K.E=
`1/2 MV^2`

`7.8792=(1)/(2)(13.4)V^2`

`V^2=7.8792* 2/13.4=1.176`

`V=1.0844m/s`

Using conservation of linear momentum

`mu+ m'v=MV`

`13(0)+0.4v=13.4(1.0844)`

`0.4v=14.53`

`v=(14.53)/(0.4)`

`v=36.3m/s`

Hence, the initial speed of the putty=36.3m/s